Archie Mobile Company has a few mobile phone service plans. Plan A offers 160 SMS and 60 minutes of talk time for $10.40. Plan B offers 280 SMS and 110 minutes of talk time for $18.40. Archie Mobile Company is also going to launch Plan C which offers 160 SMS and 290 minutes of talk time. How much should Archie Mobile Company charge for Plan C if the cost per SMS and the cost per minute of talk time do not vary across the three plans?
$1 = 100¢

Plan A = 160 SMS + 60 min = 1040 --- (1)

Plan B = 280 SMS + 110 min = 1840 --- (2)

Make the cost of SMS the same.

(1)_x7
1120 SMS + 420 min = 7280 --- (3)

(2)_x4
1120 SMS + 440 min = 7360 --- (4)

(4) - (3)
440 min - 420 min = 7360 - 7280
20 min = 80

1 min = 80 ÷ 20 = 4

60 min = 60 x 4 = 240

From (1):
160 SMS + 60 min = 1040 
160 SMS + 60 x 4 = 1040
160 SMS + 240 = 1040
160 SMS = 1040 - 240
160 SMS = 800

1 SMS = 800 ÷ 160 = 5

160 SMS
= 160 x 5
= 800

290 min
= 290 x 4
= 1160

Charges for Plan C
= 160 SMS + 290 min
= 800 + 1160
= 1960¢

1960¢ = 1960 ÷ 100 = $19.60

Answer(s): $19.60